Details

sample83.0ms

Algorithm

intervals

Results

54.0ms	181×	body	1280	valid
7.0ms	267×	body	80	valid
6.0ms	38×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify227.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1454	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.1b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
58.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series67.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
55.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367

prune160.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-r`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`associate-l` `prod-exp` `unswap-sqr`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 37

Calls

2 calls:

0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
14.0ms	(* 1/12 (pow x 4))

series153.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))

simplify86.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	123	177
1	469	163
2	2175	160
3	5002	160

prune106.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
4.4b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`add-exp-log` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `associate-r` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

9.0ms	(+ (exp x) 2.0)
20.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
37.0ms	(* (+ (exp x) 2.0) (exp x))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series329.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (exp x) 2.0)
213.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
21.0ms	(* (+ (exp x) 2.0) (exp x))
87.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	312	834
1	1220	713
2	5001	710

prune248.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) 2.0))
0.0b	(sqrt (+ (exp x) 2.0))
1.0b	(* (* (sqrt (+ (exp x) 2.0)) (sqrt (exp x))) (* (sqrt (+ (exp x) 2.0)) (sqrt (exp x))))
4.4b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
35×	`pow-prod-down`
18×	`sqrt-pow1` `pow1/2`
16×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`flip3-+` `prod-exp` `sqrt-prod` `pow-prod-up` `cbrt-unprod` `flip-+`
6×	`add-cube-cbrt` `pow-sqr`
5×	`sqrt-unprod`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow-plus` `associate-*r/` `hypot-def` `distribute-lft-out`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `rem-square-sqrt` `*-commutative` `fma-udef`

Counts

4 → 102

Calls

4 calls:

12.0ms	(sqrt (+ (exp x) 2.0))
12.0ms	(sqrt (+ (exp x) 2.0))
134.0ms	(* (* (sqrt (+ (exp x) 2.0)) (sqrt (exp x))) (* (sqrt (+ (exp x) 2.0)) (sqrt (exp x))))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series174.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ (exp x) 2.0))
35.0ms	(sqrt (+ (exp x) 2.0))
21.0ms	(* (* (sqrt (+ (exp x) 2.0)) (sqrt (exp x))) (* (sqrt (+ (exp x) 2.0)) (sqrt (exp x))))
89.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	343	843
1	1277	653
2	5002	632

prune307.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes16.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.7s	5686×	body	1280	valid
204.0ms	1243×	body	640	valid
203.0ms	8425×	body	80	valid
60.0ms	613×	body	320	valid
19.0ms	300×	body	160	valid